No Soldier shall, in time of peace be quartered in any house, without the consent of the Owner, nor in time of war, but in a manner to be prescribed by law.
One earlier commentator noted this spoke of a principle holding: "The billeting of soldiers upon the citizens of a state, has been generally found burthensome to the people, and so far as this article may prevent that evil it may be deemed valuable; but it certainly adds nothing to the national security." More recently, it was understood to "reflect a traditional and strong resistance of Americans to any military intrusion into civilian affairs."
The amendment, specifically addressing something ever more upsetting on principle than in actuality (first choice for quartering British troops was not the home, but inns and so forth), spoke of a broader principle: the civil is supreme over the military power. Per the Declaration of Independence:
He has kept among us, in times of peace, Standing Armies, without the Consent of our legislatures.--He has affected to render the Military independent of and superior to the Civil power. . . . --For quartering large bodies of armed troops among us:--For protecting them, by a mock Trial, from punishment for any Murders which they should commit on the Inhabitants of these States
Ultimately, this practice that was quite upsetting to the colonialists, was largely forgotten ... at least the Third Amendment itself. The amendment was mentioned a few times in passing as securing privacy and civil control (including during war time ... "the law" dictated by Congress ... see Hamdan), but the principles at its core remains very important.
A principle honored in the Second Amendment as well, honoring "militia" called for temporary service over a permanent standing army. A principle suggesting why the South shunned federal troops after the Civil War. Why our troops in Iraq is such a problem. Why the use of Israeli troops in the current mess, at best excessive if to some degree understandable, is so problematic [as in Iraq, troops lead to a slew of problems, not always intentionally criminal]. And so forth.
And, a principle, as noted, suggesting why even now,* civil "law" needs to be supreme.
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* Various people have discussed whether the 3A and other areas of the Constitution understands some nether region between "peace" and "war" [e.g., habeas was been suspended during the Reconstruction]. And, Hamdan notes:
The Court is correct to concentrate on one provision of the law of war that is applicable to our Nation's armed conflict with al Qaeda in Afghanistan and, as a result, to the use of a military commission to try Hamdan.
Some argue we are not "at war" in Iraqi and/or Afghanistan. The SC left that an open question (the quote is from Kennedy's concurrence, who notes it is "a conflict that continues as we speak"). But, even in war, "the law" holds.